Answer:
Angular velocity, [tex]\omega=3747.33\ rev/min[/tex]
Explanation:
In this case, we need to find the angular speed needed for a centrifuge to produce an acceleration of 759 times the gravitational acceleration.
Radius of the circular path, r = 4.83 cm
The acceleration acting on the particle in circular path is given by :
[tex]a=r\omega^2[/tex]
[tex]\omega[/tex] is the angular speed in rad/s
[tex]\omega=\sqrt{\dfrac{a}{r}}[/tex]
[tex]\omega=\sqrt{\dfrac{759\times 9.8}{4.83\times 10^{-2}}}[/tex]
[tex]\omega=392.42\ rad/s[/tex]
or
[tex]\omega=3747.33\ rev/min[/tex]
So, there are 3747.33 revolutions per minute that is needed. Hence, this is the required solution.
